The $N$-soliton solutions for coupled modified Yajima–Oikawa system via the Riemann–Hilbert method

Tanlin Li, Yuxuan Li, Lin Huang

School of Mathematical Sciences, Hangzhou Dianzi University, Zhejiang, China

Abstract: We establish a rigorous Riemann–Hilbert (RH) framework for the coupled modified Yajima–Oikawa system. Unlike conventional approaches that initiate spectral analysis with the spatial Lax operator, we employ its temporal counterpart to derive the requisite analytic spectral functions and thereby formulate the associated RH problem. We then obtain explicit multi-soliton solutions in the reflectionless case. Leveraging symbolic computations in Maple, we analyze the ensuing soliton dynamics and illustrate their interactions. Our RH methodology not only elucidates the intricate spectral features of the coupled modified Yajima–Oikawa system but also provides a systematic procedure for constructing its general $N$-soliton solutions.

Keywords: coupled modified Yajima–Oikawa system, Riemann–Hilbert approach, multi-soliton solutions.

MSC: 35Q15; 35Q51

Received: 06.07.2025
Revised: 06.07.2025

DOI: 10.4213/tmf11042

 English version: Theoretical and Mathematical Physics, 2026, 226:1, 97–108

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